Should I rent to an unmarried couple where only one works?

[Dennis Adams]

The couple claims to be married and the wife says she's been a SAHM for 10 years but a quick internet search shows them having seperate addresses 2 years ago.  I'm concerned that if the kids are hers, they're really not married and she has no income, then he could leave without any financial obligation to her and I'd be stuck with a family I'd have to evict.  He makes enough money and they both claim to have no credit problems and excellent references.  Thoughts?  I haven't done a credit or background check yet - would like to decide whether to accept this kind of situation before I do that.  This is our only rental and it's recently renovated in a medium sized town so the rental market isn't super active right now.  Thanks for any insight from more experienced landlords